Christine Lagarde shares a platform in Washington with Hillary Clinton, the US secretary of state. Photograph: Benjamin J Myers/Corbis

The world risks sliding into a 1930s-style slump unless countries settle their differences and work together to tackle Europe's deepening debt crisis, the head of the International Monetary Fund has warned.

On a day that saw an escalation in the tit-for-tat trade battle between China and the United States and a deepening of the diplomatic rift between Britain and France, Christine Lagarde issued her strongest warning yet about the health of the global economy and said if the international community failed to co-operate the risk was of "retraction, rising protectionism, isolation".

She added: "This is exactly the description of what happened in the 1930s, and what followed is not something we are looking forward to."

The IMF managing director's call came amid growing concern that 2012 will see Europe slide into a double-dip recession, with knock-on effects for the rest of the global economy. "The world economic outlook at the moment is not particularly rosy. It is quite gloomy," she said.

Since arriving in Washington in the summer, Lagarde has been forced to cut her organisation's forecasts for global growth next year and is now putting pressure on countries outside the eurozone – including Britain – to play their part in containing Europe's sovereign debt crisis.

An IMF plan, agreed at the Brussels summit last week, involves obtaining €200bn (£168bn) from European countries and then asking the rest of the world to contribute. Beijing has so far proved reluctant to join in a rescue of the eurozone and has said it is up to Europe to sort out its own problems.

Speaking at the State Department in Washington, Lagarde said: "There is no economy in the world, whether low-income countries, emerging markets, middle-income countries or super-advanced economies, that will be immune to the crisis that we see not only unfolding but escalating.

"It is not a crisis that will be resolved by one group of countries taking action. It is going to be hopefully resolved by all countries, all regions, all categories of countries actually taking some action."

Lagarde said that the scale of the eurozone crisis, and its implications for other countries, meant that Europe's governments could not tackle it alone. "It is going to require efforts, it is going to require adjustment; and clearly it is going to have to start from the core of the crisis at the moment, which is obviously the European countries, and in particular the countries of the eurozone," Lagarde said.

As Lagarde called for unity, there were strong attacks on Britain from both the French finance minister, Francois Baroin, and the governor of the French central bank, Christian Noyer, in what appeared to be a concerted attempt by Paris to escalate a war of words with London in the wake of Britain's decision to veto a new EU treaty.

Noyer, speaking amid financial market speculation that the Standard & Poor's ratings agency was about to strip France of its coveted AAA rating, said Britain's credit rating should be downgraded first.

He said a downgrade for France (which would drive up the interest Paris pays to borrow, and make loans in the wider economy more expensive) "doesn't strike me as justified based on economic fundamentals.

"If it is, they should start by downgrading the UK, which has a bigger deficit, as much debt, more inflation, weaker growth, and where bank lending is collapsing."

In strikingly similar language, Baroin poked fun at David Cameron in a speech to the French parliament. "Great Britain is in a very difficult economic situation: a deficit close to the level of Greece, debt equivalent to our own, much higher inflation prospects, and growth forecasts well under the eurozone average. It is an audacious choice the UK government has made."

Downing Street responded with restraint. Cameron's official spokesman said: "We have put in place a credible plan for dealing with our deficit, and the credibility of that plan can be seen in what has happened to bond yields in this country." Privately, officials said it was a "strange thing" for Noyer to speak as he did, but there was no desire in London to inflame the situation.

In another sign the financial crisis was deepening last night, Fitch cut its ratings on eight of the world's biggest banks, including Barclays, Bank of America, and Deutsche Bank. It warned that they all faced "increased challenges", with potential losses hard to calculate.

John Bryson, the US commerce secretary, signalled that Washington would retaliate against Beijing's decision to put tariffs on high-performance US cars imported into China. "The United States has reached a point where we cannot quietly accept China ignoring many of the trade rules. China still substantially subsidises its own companies, discriminates against foreign companies, and has poor intellectual property protections," he said.

Britain has been given observer status on a working group set up by the Economic and Financial Committee of the EU to carry out technical work ahead of the full-blown negotiations on the treaty, boosting Cameron's claim that Britain has not been marginalised by his move last week.

On Thursday Hungary and the Czech Republic raised doubts about the proposed agreement, saying they would not sign the new treaty if they had to give up their right to decide tax policy. Downing Street denied that Cameron was attempting to foment opposition to the treaty, and said that the prime minister was talking to all sides. But by Thursday the only eurozone leader he had spoken to was Enda Kenny, the Irish prime minister.